To get steady states, do I just set for both models?
I'm not sure how to get stability. Do I just take the derivative of both models and plug in the steady states?

Linearise about the steady state and either solve the linearised equation, if you have a growing solution you have instability. Alternativly just examin the linearised equation to determine the stability of the steady state.

In these cases the steady state appears to be , and for a small departure from the steady state the departure grows if and respectivly.